The former Anglican archbishop of Cape Town Desmond Tutu waits to receive the 2013 Templeton Prize at the Guildhall in central London in this file photo dated May 21, 2013. REUTERS/Paul Hackett/File Photo

CAPE TOWN (Reuters) - South African anti-apartheid activist and veteran cleric, Archbishop Desmond Tutu, was responding well to a new course of antibiotics, his daughter said on Tuesday, following social media reports her father had died.

The 84-year-old Nobel Peace Prize winner, who has struggled with ill health in recent years, was re-admitted to hospital on Saturday to treat an infection following surgery last week.

"He is in very good spirits and much more like himself than he has been," Reverend Canon Mpho Tutu van Furth told a media briefing, adding that her father could leave hospital soon.

"The hoax messages are very disturbing and incredibly unkind... It is very distressing to hear that kind of news over Twitter, particularly for family," Mpho said, referring to social media reports on Tutu's premature death.

Tutu spoke against white-minority rule from his pulpit, earning him global acclaim.